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<a name="Multi_002ddimensional-MPI-DFTs-of-Real-Data"></a>
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<p>
Next: <a href="Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms.html#Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms" accesskey="n" rel="next">Other Multi-dimensional Real-data MPI Transforms</a>, Previous: <a href="MPI-Data-Distribution.html#MPI-Data-Distribution" accesskey="p" rel="prev">MPI Data Distribution</a>, Up: <a href="Distributed_002dmemory-FFTW-with-MPI.html#Distributed_002dmemory-FFTW-with-MPI" accesskey="u" rel="up">Distributed-memory FFTW with MPI</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Multi_002ddimensional-MPI-DFTs-of-Real-Data-1"></a>
<h3 class="section">6.5 Multi-dimensional MPI DFTs of Real Data</h3>

<p>FFTW&rsquo;s MPI interface also supports multi-dimensional DFTs of real
data, similar to the serial r2c and c2r interfaces.  (Parallel
one-dimensional real-data DFTs are not currently supported; you must
use a complex transform and set the imaginary parts of the inputs to
zero.)
</p>
<p>The key points to understand for r2c and c2r MPI transforms (compared
to the MPI complex DFTs or the serial r2c/c2r transforms), are:
</p>
<ul>
<li> Just as for serial transforms, r2c/c2r DFTs transform n<sub>0</sub>&nbsp;&times;&nbsp;n<sub>1</sub>&nbsp;&times;&nbsp;n<sub>2</sub>&nbsp;&times;&nbsp;&hellip;&nbsp;&times;&nbsp;n<sub>d-1</sub>
 real
data to/from n<sub>0</sub>&nbsp;&times;&nbsp;n<sub>1</sub>&nbsp;&times;&nbsp;n<sub>2</sub>&nbsp;&times;&nbsp;&hellip;&nbsp;&times;&nbsp;(n<sub>d-1</sub>/2 + 1)
 complex data: the last dimension of the
complex data is cut in half (rounded down), plus one.  As for the
serial transforms, the sizes you pass to the &lsquo;<samp>plan_dft_r2c</samp>&rsquo; and
&lsquo;<samp>plan_dft_c2r</samp>&rsquo; are the n<sub>0</sub>&nbsp;&times;&nbsp;n<sub>1</sub>&nbsp;&times;&nbsp;n<sub>2</sub>&nbsp;&times;&nbsp;&hellip;&nbsp;&times;&nbsp;n<sub>d-1</sub>
 dimensions of the real data.

</li><li> <a name="index-padding-4"></a>
Although the real data is <em>conceptually</em> n<sub>0</sub>&nbsp;&times;&nbsp;n<sub>1</sub>&nbsp;&times;&nbsp;n<sub>2</sub>&nbsp;&times;&nbsp;&hellip;&nbsp;&times;&nbsp;n<sub>d-1</sub>
, it is
<em>physically</em> stored as an n<sub>0</sub>&nbsp;&times;&nbsp;n<sub>1</sub>&nbsp;&times;&nbsp;n<sub>2</sub>&nbsp;&times;&nbsp;&hellip;&nbsp;&times;&nbsp;[2&nbsp;(n<sub>d-1</sub>/2 + 1)]
 array, where the last
dimension has been <em>padded</em> to make it the same size as the
complex output.  This is much like the in-place serial r2c/c2r
interface (see <a href="Multi_002dDimensional-DFTs-of-Real-Data.html#Multi_002dDimensional-DFTs-of-Real-Data">Multi-Dimensional DFTs of Real Data</a>), except that
in MPI the padding is required even for out-of-place data.  The extra
padding numbers are ignored by FFTW (they are <em>not</em> like
zero-padding the transform to a larger size); they are only used to
determine the data layout.

</li><li> <a name="index-data-distribution-3"></a>
The data distribution in MPI for <em>both</em> the real and complex data
is determined by the shape of the <em>complex</em> data.  That is, you
call the appropriate &lsquo;<samp>local size</samp>&rsquo; function for the n<sub>0</sub>&nbsp;&times;&nbsp;n<sub>1</sub>&nbsp;&times;&nbsp;n<sub>2</sub>&nbsp;&times;&nbsp;&hellip;&nbsp;&times;&nbsp;(n<sub>d-1</sub>/2 + 1)

complex data, and then use the <em>same</em> distribution for the real
data except that the last complex dimension is replaced by a (padded)
real dimension of twice the length.

</li></ul>

<p>For example suppose we are performing an out-of-place r2c transform of
L&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N
 real data [padded to L&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;2(N/2+1)
],
resulting in L&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N/2+1
 complex data.  Similar to the
example in <a href="2d-MPI-example.html#g_t2d-MPI-example">2d MPI example</a>, we might do something like:
</p>
<div class="example">
<pre class="example">#include &lt;fftw3-mpi.h&gt;

int main(int argc, char **argv)
{
    const ptrdiff_t L = ..., M = ..., N = ...;
    fftw_plan plan;
    double *rin;
    fftw_complex *cout;
    ptrdiff_t alloc_local, local_n0, local_0_start, i, j, k;

    MPI_Init(&amp;argc, &amp;argv);
    fftw_mpi_init();

    /* <span class="roman">get local data size and allocate</span> */
    alloc_local = fftw_mpi_local_size_3d(L, M, N/2+1, MPI_COMM_WORLD,
                                         &amp;local_n0, &amp;local_0_start);
    rin = fftw_alloc_real(2 * alloc_local);
    cout = fftw_alloc_complex(alloc_local);

    /* <span class="roman">create plan for out-of-place r2c DFT</span> */
    plan = fftw_mpi_plan_dft_r2c_3d(L, M, N, rin, cout, MPI_COMM_WORLD,
                                    FFTW_MEASURE);

    /* <span class="roman">initialize rin to some function</span> my_func(x,y,z) */
    for (i = 0; i &lt; local_n0; ++i)
       for (j = 0; j &lt; M; ++j)
         for (k = 0; k &lt; N; ++k)
       rin[(i*M + j) * (2*(N/2+1)) + k] = my_func(local_0_start+i, j, k);

    /* <span class="roman">compute transforms as many times as desired</span> */
    fftw_execute(plan);

    fftw_destroy_plan(plan);

    MPI_Finalize();
}
</pre></div>

<a name="index-fftw_005falloc_005freal-2"></a>
<a name="index-row_002dmajor-5"></a>
<p>Note that we allocated <code>rin</code> using <code>fftw_alloc_real</code> with an
argument of <code>2 * alloc_local</code>: since <code>alloc_local</code> is the
number of <em>complex</em> values to allocate, the number of <em>real</em>
values is twice as many.  The <code>rin</code> array is then
local_n0&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;2(N/2+1)
 in row-major order, so its
<code>(i,j,k)</code> element is at the index <code>(i*M + j) * (2*(N/2+1)) +
k</code> (see <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>).
</p>
<a name="index-transpose-1"></a>
<a name="index-FFTW_005fTRANSPOSED_005fOUT"></a>
<a name="index-FFTW_005fTRANSPOSED_005fIN"></a>
<p>As for the complex transforms, improved performance can be obtained by
specifying that the output is the transpose of the input or vice versa
(see <a href="Transposed-distributions.html#Transposed-distributions">Transposed distributions</a>).  In our L&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N
 r2c
example, including <code>FFTW_TRANSPOSED_OUT</code> in the flags means that
the input would be a padded L&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;2(N/2+1)
 real array
distributed over the <code>L</code> dimension, while the output would be a
M&nbsp;&times;&nbsp;L&nbsp;&times;&nbsp;N/2+1
 complex array distributed over the <code>M</code>
dimension.  To perform the inverse c2r transform with the same data
distributions, you would use the <code>FFTW_TRANSPOSED_IN</code> flag.
</p>
<hr>
<div class="header">
<p>
Next: <a href="Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms.html#Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms" accesskey="n" rel="next">Other Multi-dimensional Real-data MPI Transforms</a>, Previous: <a href="MPI-Data-Distribution.html#MPI-Data-Distribution" accesskey="p" rel="prev">MPI Data Distribution</a>, Up: <a href="Distributed_002dmemory-FFTW-with-MPI.html#Distributed_002dmemory-FFTW-with-MPI" accesskey="u" rel="up">Distributed-memory FFTW with MPI</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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